Abstract
The aim of this paper is mainly to study the (L, M)-fuzzy measurability in view of degree. Firstly, we generalize the notion of (L, M)-fuzzy σ-algebra by defining the degree of an (L, M)-fuzzy σ-algebra with respect to a mapping σ : L X ⟶ M. Such kind of degrees is proved to satisfy some axioms of (L, M)-fuzzy σ-algebra. Additionally, we define and study some special degrees such as the degree of (L, M)-fuzzy measurable mapping, (L, M)-fuzzy measurable-to-measurable mapping, isomorphic mapping and quotient mapping with respect to mappings between two (L, M)-fuzzy measurable spaces in details. Finally, we give characterizations of these degrees and investigate the relationships between them.
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